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comment Deriving the Angular Momentum Commutator Relations by using $\epsilon_{ijk}$ Identities
Argue that (ijk) -> (xyz) and that the same answer holds for (jki) -> (yzx) etc. Changing the indices doesn't change the solution, for any permutation. You could write it out, explaining, or you could actually show the permutations are the same simply.
May
26
answered Deriving the Angular Momentum Commutator Relations by using $\epsilon_{ijk}$ Identities
May
21
accepted Inelastic Scattering and coherent scatterng
May
13
awarded  Yearling
Apr
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awarded  Fanatic
Feb
21
comment Supplements for Kittel's Solid State Physics?
Condensed Matter Physics by Marder may also interest you, but I think his section on crystallography is tiny.
Feb
21
answered Supplements for Kittel's Solid State Physics?
Feb
17
comment Rewriting Creation and Annihilation Operators
Thanks so much for your help KDN. Awesome
Feb
17
accepted Rewriting Creation and Annihilation Operators
Feb
17
comment Rewriting Creation and Annihilation Operators
of course, it is 1. $$[a,a^{\dagger}]=1$$
Feb
17
comment Rewriting Creation and Annihilation Operators
I'm afraid it doesn't.
Feb
17
comment Rewriting Creation and Annihilation Operators
Great call, hadn't even considered it in my foolishness. $$[p_{i},r_{j}]=[p_{i},r_{j}]=-i\hbar \delta_{ij}$$ $$[R_{i},\pi_{j}]=0$$ $$[\pi_{i},\pi_{j}]=-i \epsilon_{ij} m \hbar \omega_{c}=-i \epsilon_{ij} \frac{\hbar^{2}}{l_{b}^{2}}$$ $$[R_{i},R_{j}]=i \epsilon_{ij} l_{b}^{2}$$ $$[\rho_{i},\rho_{j}]=-i \epsilon_{ij} l_{b}^{2}$$ $$[\rho_{i},\pi_{j}]=i \hbar \delta_{ij}$$ $$[p_{i},\pi_{j}]=-i \hbar \frac{e}{c} \frac{\partial A_{j}}{\partial r_{i}}$$ $$[R_{i},r_{j}]=i \epsilon_{ij} l_{b}^{2}$$ $$[\rho_{i},r_{j}]=-i \epsilon_{ij} l_{b}^{2}$$
Feb
17
comment Rewriting Creation and Annihilation Operators
For context, I am studying the quantum Hall Effect, integer and fractional, and this came up in my instructors online notes. I am unsure why you would rewrite this, and further what is the best way to approach it. To expand on my idea, I was thinking to expand $\pi$ to $\vec{\pi}=m\vec{v}=\vec{p}-\frac{q}{c}\vec{A}$ and perhaps try from there.
Feb
17
asked Rewriting Creation and Annihilation Operators
Feb
12
answered Projectile motion, canon vs cliff
Feb
12
comment Projectile motion, canon vs cliff
Working on this now. Also, the velocity of the ball at the top of the cliff is zero because if it were not, it would go higher than 85m; the question tells you it just reaches the top.
Feb
12
answered How can I understand work conceptually?